There is known a Diesel engine with turbocharger, in which an exhaust shutter is provided in the exhaust path in order to apply engine brake. In supercharging pressure control apparatuses applied to such the engine, there is known a supercharging pressure control apparatus including a pressure container connected to the exhaust path between the exhaust shutter and an exhaust valve. In the supercharging pressure control apparatus, an exhaust pressure is accumulated in the pressure container when the exhaust shutter is closed to increase the exhaust pressure, and the exhaust pressure injected from the pressure container when a turbine of the turbocharger needs to be accelerated (see Patent Document 1). In addition, there are Patent Documents 2 and 3 as prior art references in relation to the present invention.